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Author:   Lorenz J. Halbeisen
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   2nd ed. 2017
Weight:   1.075kg
ISBN:  

9783319602301

ISBN 10:   3319602306
Pages:   594
Publication Date:   11 January 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.
Language:   English

Table of Contents

The Setting.- First-Order Logic in a Nutshell.- Axioms of Set Theory.- Overture: Ramsey's Theorem.- Cardinal Relations in ZF Only.- Forms of Choice.- How to Make Two Balls from One.- Models of Set Theory with Atoms.- Thirteen Cardinals and Their Relations.- The Shattering Number Revisited.- Happy Families and Their Relatives.- Coda: A Dual Form of Ramsey’s Theorem.- The Idea of Forcing.- Martin's Axiom.- The Notion of Forcing.- Proving Unprovability.- Models in Which AC Fails.- Combining Forcing Notions.- Models in Which p=c.- Suslin’s Problem.- Properties of Forcing Extensions.- Cohen Forcing Revisited.- Sacks Forcing.- Silver-Like Forcing Notions.- Miller Forcing.- Mathias Forcing.- How Many Ramsey Ultrafilters Exist?.- Combinatorial Properties of Sets of Partitions.- Suite.

Reviews

Each chapter ends with Notes that often add historical information, offer further remarks on the chapter's contents ... . Halbheisen's Combinatorial Set Theory is an excellent source for the intermediate or advanced student of set theory ... Because of its wealth of material, it should also serve as an excellent resource for those designing advanced courses or searching for seminar assignments for students. (J. M. Plotkin, zbMATH 06755662, 2018)

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